Logic (2016)
41. Aquinas's Order of God's Attributes in the Two Summas; Testing Syllogisms in the First and Second Figures
Class of 2017-03-30
https://berquistcourse.com/course/philosophy/2-logic-2016/041-aquinass-order-of-gods-attributes-in-the-two-summas-testing/

[0:00] I was thinking, you know, what what I should do for if I go and do the same Thomas Day speech there, you know, and thinking of something I worked on before, the comparing two treatises on the substance of God, right? Huh? Now, in the two treatises on the substance of God, it has five parts, right? Like in the Summa Theologiae he shows that God is what altogether simple first.

[0:32] Then he shows that God is perfect, right, and hence good. He's attached to that, and then he shows that God is what infinite. Then he shows that God is unchanging in no way moving, and then finally God is one. He has the same five in the Summa Contra Gentiles, right? Er, yeah. And he says, "Not quite the same order, right? " Come to that, right? And he says,

[1:06] "Calls out the substance of God, right? " Okay. Then the Darian talks about what God does, right? His operations, right? Well, I was thinking, you know, of why he he

[1:26] in both works he takes the simplicity of God and the perfection of God right next to each other, and the simplicity of God before his perfection. That's common to both. And they say, "I can't stand the idea of five, right? " That's always my favorite number. Yeah, I do kind of like it. You know, it's kind of interesting. You know, you know, in the in this in both Summas too, when he takes up the existence of God before when God exists, he gets five arguments, right?

[2:04] And he gets a substance, yes, five, right? Okay. It's all the same. Would you divide those five into two or three? What do you think?

[2:25] Maybe you can do both. Well, I think you could divide them maybe into three, right? How to get that right? Well, when Thomas talks about simple and what perfect, right? He makes the point in Summa Theologiae that

[2:50] this is just the reverse of what you find in the material world. The square, I mean, the stone is more simple than the tree, but which is more perfect? Tree. Yeah. And the tree is more simple than the dog or the cat, but which is more perfect? Dog. Yeah. And man is more what complicated than even the dog or the cat,

[3:19] and but he's what yeah. I say, but God is most simple and most what perfect. So Thomas kind of makes the point, you know, that if you take up the simplicity argument, so we can't be perfect in the simplest things. And where did I came from? I came from the material world, did you? Oh, just uh, this is uh, one of the uh, weak points you could say in Dawkins and the other atheists' arguments about God, because they assume that he has to be complex.

[3:52] Yeah, to be perfect. To be perfect in order to yeah, yeah. So Thomas says it's appropriate we talk about perfection of God right after we talk about being simple, right? Because when you get into any kind of composition, if you find creatures, right, but then you think you got to negate what perfection too, and so

[4:12] you got to negate you got to talk about perfection of God next, right? So he's just kind of tying those two together, right? And in both sumas, they're taken up next to each other, right? And the simplicity before the perfection, right?

[4:24] Okay. And then I thought of a clever thing, right? As in making a ascent like Dante, you know. You know Dante ascends from what? Through hell up through what? Up to heaven, right? So he's ascending from the lower to the the higher, obviously, right? And I said, if you go up, if if I, you know, my great angel would reveal himself a little bit more, right? Okay.

[4:50] And then he introduced me to an archangel, and we go up the scale, right? As you go up the scale, you find that the angels are getting more and more perfect, okay? But they're also getting what? Simpler. Yeah. Yeah. So Thomas points out, you know, he compares God and the angels, right? God, by understanding himself, understands everything else. The very the angels understand themselves very well, right?

[5:20] They're substance much more than you understand your soul, but they don't what understand everything else by understanding themselves, and so they need some other thoughts besides what they know for themselves. But the higher angels, right, have fewer thoughts than the lower angels, but they understand more perfectly with fewer thoughts. So as as we in a kind of Dante-like recession and sin, right, the angels what get simpler and simpler and more and more perfect.

[5:54] So to be more and more simple and more perfect, right, go right together all the way up from the angels up to the archangels, princes, you know, the what? Virtues of the powers, the virtues and the what? The lords and the dominus, and then the thrones and the cherubim and the seraphim, right? What do you expect to get big at the end there? Something most simple and most perfect.

[6:23] They kind of you know it seems to be the same order, right, in the immaterial world. The more simple something is, the more perfect it is, and the more perfect it is, the more what simple it is, right? Just like Aristotle said that tragedy is better than what epic, it's it's more simple, more perfect form of fiction, right? Kind of amazing thing, even though he said Homer is the poet, right?

[6:51] But Sophocles comes close, right? But the form of tragedy is better, it's more simple. Okay. You remark upon this on Mozart's famous work, how simple it is.

[7:07] But the pianist told me you have to practice longer to play a Mozart piece you know, because everything's got to just... Okay. So maybe those two belong together, right? The simplicity of God and perfection of God. They're talked about together, right? And Thomas makes that point, right? But I can make it much more important by this. He sent us the angels, right? Wow! The more we love, the more perfectly we become, and the simpler they become.

[7:37] That's just amazing, right? So in God, you know, put those two together, right? Well, then Thomas in the what? In the uh, Summa Contra Gentiles, after he takes up the simplicity and perfection of God, he takes up the unity of God and the infinity of God. Say, well, this is gonna make a couple out of them too, right? Not married, but a couple anyway. And

[8:16] God is one and infinite, and mathematically that makes sense. They go together, right? One and infinite, right? But there's, in a sense, one and infinite. The order which he gives them there in the Sumo Contra Gentiles, correspond to the order of simple and perfect.

[8:45] Well, give you our little secret now, right? Thomas's assistant there, right? Who went with him all the time, right? He says to Thomas, "Could you write kind of a simple, you know, exposition of the faith and so on that I could carry with me in my spare moments, you know? " Okay, so Thomason of course, so I go with the compendium of what theology, right? Which is a more brief consideration of things and so on.

[9:13] And what do you think he does in the middle of the consideration of simplicity of God? He talks about this unity of God. Oh, so one in some way corresponds to simplicity, right? Okay. And the reason why there could be only one God is because he's entirely simple. The reason why there can be many men is because we're, you know, we've got this individual matter and so on, composed and what a man is and so on.

[9:40] Okay. Now I was asking my student last night, but I think the the the just see if they would agree with me, you know. Would you say that God's simplicity is endless? So much would you say God's perfection is endless? What would you be more apt to say? Perfection without limits Yeah, yeah. God's perfection is endless. You're never going to be bored again, see him, right? Or even you talk about goodness, which is attached to perfection.

[10:19] God's goodness is what endless, right? It's not just like the like the. You know, you could say you know that the the uh... cherubim are more perfect than the thrones, but not as perfect as.

[10:41] But can you see how how good God is, how perfect God is? You know, in in the second, in the fourth letter of the Council, it is. they take as an attribute of God that he's immensus And this is almost like a synonym for. eternal, It doesn't come with it right? You know, even you know if you take the universe, if the universe was was in fact infinite in extent, right?

[11:09] Could would be measurable. In that sense, even think it. So can we say how perfect God is? Right, His perfections endless, right? Okay. I mean Thomas,

[11:25] it seems like could God make everything He's able to make? Well, if you take it one by one, He can always make it. He's able to make. But could He make everything He's able to make for you? No, because then He'd have a limit. That's amazing. This thing, right? So I said, in a sense, is it by chance that Thomas actually talks about in the Summa Con Gentiles, my favorite book.

[11:51] If he talks about the simplicity and perfection of God, right, and he follows that with his what, unity and infinity in that what order? Order, right. So those two belong together, right? And they kind of correspond to that debate. So just shown by the fact that that these the unity of God is considered in the simplicity of God with this Compendium theology, right? Okay. In fact, I asked him last night.

[12:19] Just didn't have students because it was on my mind. I was thinking about what I was going to do with the out there. And it's kind of amazing, you know. I'll admit that that I would think of the perfection of God or the goodness of God as being endless more than His simplicity is. Sometimes strange to see endless simplicity, right? You know, I'd say, well, He's completely simple, right?

[12:40] Altogether simple, or something, you know. I'd say, but His perfections, His His goodness is is endless, you know. How good is God? You can't say. I mean, He's beyond anything, right? You want to see in the Psalms, you know, praise Him as much as you can, because He's He's beyond all praise, right? You can't say what you know. You can say you know how much praise Mr.

[13:02] Nixon deserves, or how much praise you know. You know, I praise my teacher Kasurik and my teacher, you know, but I praise De Koninck even more, you know. And you know,

[13:17] Kasurik said that compared to Aristotle, I got the greatest. Engorm, I praise Aristotle even more highly than I would praise you know Kasurik, right? You know, I praise him. So you can see how much I should praise these guys, right? You know. But

[13:33] how much how much did you praise God? But you're praising him because of his what? Not so much because simplicity, right? More because of his perfection, his his goodness, right? He's the good of every good, as Thomas said, right? Augustine said first, okay.

[13:55] But now in the order in the Summa is a little bit different, right? In the Summa, he talks about the unity of God and the infinity of God after the simplicity and the perfection, right? He talks about the what? The infinity of God, right after he talks about what? The perfection of God, confirmation that goes more with that, right? Okay. But he takes up the what? Unity last.

[14:32] Oh, is Thomas just not as good at orders he has in the Summa Contra Gentiles, right? Or is there a reason why he put the infinity right next to what? The perfection because of that connection that we all saw, right? But is there also reason why he put the what? Unity last rather than you know up there with corresponding to the simplicity, right? Well, when you study theology, I've seen it, you know.

[15:06] I think you may be seen too. You see them that we're considering de Deo uno et trino. Do you remember that? Right. Have you seen that? And he wants to

[15:22] distinguish between the way he's one and the way he's three, right? So it's appropriate when he gets through at De Deo Uno that he would last what? God is one. See, in the Summa, right? Because in the in the prima pars he's going to go on to Trinity, right? So the last thing he wants to emphasize in the substance of God is that he's what? One. So you don't say you know whatever it's the other infinity, it's not going to contradict.

[15:50] That's just one God, right? We're not polytheists, so. See? Why in the Summa Contra Gentiles? oh, we don't talk about the Trinity, you know, in the first three books because we're going to talk about things that natural reason can know as well as by faith we can know, right? And so we're not going to have that problem, you know, that you have where in the prima pars you talk about the Trinity as well as as De Deo Uno, right?

[16:20] So kind of emphasize that last, right? Okay. But then the wild card is what? God is unchanging, right? And in the Summa Contra Gentiles, that's the first thing talked about. Here, it's talked about after the infinity of God, but before his what? His unity, right?

[16:46] Really, really, really, something's out of order here, right? Okay. But if you look at the what comes before the consideration of the substance of God, it's a consideration of the what? Whether God exists, right? You had these five arguments, right? If you compare the two Summas, they both the first argument is what from motion, right? But in the case of the Summa Contra Gentiles, the first and the second argument are from motion.

[17:18] So it's twice as much. And in the explanation of the argument from motion, it's what? More expansive. huh? So Thomas will say, you know, basically the first argument is that whatever is moved is moved by another, right? And then there can't be this infinite series, right, of movers and so on, right? And he says for the first premise there are three reasons, boom, boom, boom, boom, boom. And now there's three reasons, boom, boom, boom, boom.

[17:48] You know, it's much more developed, right? So sometimes you know people who are studying the first argument in the Summa Theologiae, I refer them back to the Summa Con Gentiles because you know it's kind of like a summary of what Aristotle does in the seventh and the eighth books of Natural Hearing, right? And but more, it's a more fuller summary of it in the Summa Con Gentiles.

[18:09] So if he if he has twice as much arguments for motion, right? It seems kind of natural to first take up that God is unchanging, right? You know, emphasize the argument for the unmoved mover, twice as much there, right? And even more because he goes into details, so it's kind of a good place to begin, right? But in taking up motion after the simplicity of God, the perfection of God, and infinity of God, right?

[18:41] And I remember, when I was first studying this in Kasurik's Course, you know, it's called Natural Theology, right? So we didn't do the Trinity, but we're doing these treatises, these articles that you've been know by natural reason, you know, located in the philosophy department, right? Don't talk about the Trinity because that's that's not philosophy. But anyway, um,

[19:03] uh, yeah, three reasons for saying God is unchanging. One is that he's simple. Of course, you read the first book of Natural Hearing, right, the Physics, you see that Aristotle showing that the thing that changes has to be composed. So if you show that God is simple simple, you've got a marvelous reason for saying that it's going to be unchanging. Then you know why do why do you move somewhere?

[19:27] Because you need something, right? You lack something, right? Well, if your universe is perfect and you're the good of every good and your goodness itself, you have no need to to move or change, right? You don't need anything, right? You know, one morning I say, I'm gonna stop reading out there, you know, maybe I go to the window and look out. But God knows everything, right? So because God is infinite, I mean because God is perfect, rather, he he's not what?

[19:55] Gonna have to move at all, right? Nothing. need. What do you what do they say? What do you get a guy for Christmas? Is everything? You know, what do you what do you get God for Christmas? Yeah, yeah, what do you get God? Yeah, he doesn't need he doesn't need us, right? And then the third thing is that God is infinite, right? Even the early Greeks, you know, when they talked about beginning as being infinite, you know, they thought well, how can it move, It can't move anywhere, right?

[20:20] You know, so you get three arguments, you know, for Motion, right? So, kind of appropriate that he puts it after the three things. It helps you to understand it. So you can divide the five into two twos and the what? Wild card. The the unchanging, right? Because simplicity and perfection go together, as we know from our Sed contra angels, right? The more simple it gets, the more perfect it gets, you know.

[20:54] And the less perfect it is, the less simple it is, and so they go together, right? Isn't that quite? The thought is quite different, though, right? Simplicity isn't the same thing as perfection, but they go together, right? Verity is the soul of wit. Verity is the soul of wisdom, as Shakespeare saw, right? Wisdom is the very most perfect knowledge there is, right? What characterizes it? The fool multiplies his words.

[21:22] It says in the Bible, doesn't it? The fool multiplies. So you can divide the five into what? Two twos and one. Yeah. Interesting. Okay, So here you are with the four forms. You know, this is just the logic, right? And you think I'm enthusiastic about logic, right? How dare you say that? How dare you insult me?

[22:07] What do you need logic for? Because you don't know everything, right? And Helbert teaches us in some ways. Helbert's division is kind of, you know, seems more make more sense, you know. You know that you need logic, you know, to come to know what you don't know. And there's two kinds of unknown: simple unknown, right? And therefore, you need the art of defining, right? And then there's a complex unknown, right?

[22:32] And you need the art of reasoning. That can make sense. So it's because of my need. Now, if you're going to show it follows necessarily, you've got to go back to something that is arguments, right? And these are called in Latin the dici de omni and the dici de nullo right? But? I speak English. The said of all and the set of none, right? Okay. Now, when Aristotle takes the said of all, he says that A is said of all B, And B then A is set of whatever B is set of, right?

[23:11] Okay. Remember, we had given something like that in the categories, right? You know, animals set of dog, and dog is set of what's name this kind of dog? Yeah, the retriever. Yeah, well, then animals set of retriever, right? Okay. So if A is set of all B. And so you get the expression set of all. Then A is set of whatever B is set of. That's kind of obvious if you know what it means to say that A is set of all B, right?

[23:39] Okay. I sometimes like to state it in my great love of the A statement, right? And I say that instead of saying if A is set of all B, if every B is an A, right?

[23:54] Then whatever is a B. Yeah. Isn't that kind of obvious? If you understand what it means, that's a little bit like we're saying that if you understand, you know, what a square is and what a circle is, you can see that a square is a circle, right? If you understand what it means to say every B is an A, that means what? Every B is an A.

[24:17] It doesn't mean some are, some are not. If every B is an A, then whatever is a B. Isn't that obvious? It's known. It's a statement known to itself. I know it's a statement known to itself by all, but it's not too hard, is it? Okay. Well, here you're being told that every B is an A, right? Then whatever is a B is going to be what?

[24:46] An A. Well, it's obvious, Professor. Why do we waste our time with this stuff? Okay. So every C is A, right? Okay. I tell the students in the exam now, if it's by the set of all that you see that this follows, right? It follows necessarily, right? By the set of all. Okay. Now asking a separate question what the set of all is, right? Okay. I think it's easier to state it in the form of if every B is an A, then whatever is a B is an A, right?

[25:24] In the informal way, right? Okay. Aristotle didn't get that. Okay. Now there's another obvious thing, which is the set of none, right? So if A is set of none of the Bs, right? Then is A set of anything to which B is set of? No, because if A were set of something that B is set of, then A would not be in either of all B, would it?

[25:57] Okay. Aristotle first, right? Aristotle said that. Yes. Aristotle knew and proved. If no B is an A, right? Then whatever is a B. It's not A. Now is that if then statement in need of proof? Shouldn't be. Yeah. Okay. So if no b is an a, then it's not that means, and it should be obvious to you that whatever is a B is a what? Not A.

[26:33] An a. So since every c is a b, then how many c's are not a's? So no c is a. Okay. So I've got one way of showing you there's a affirmative, one way of showing the universal negative. Wow, what more could you ask for, right? Now if you if you went on to the ones the cases that have a what particular right statement, you know, if you had instead of every c is b, just that some c is b, what would be your conclusion?

[27:13] Some C is A. Yeah. And if instead of knowing that every c is b, you just said, well, I know some c's are b's, then those some c's being b's can't be what a's. So you'd. Have just some, C Yes some C is not A, right? Okay. So you can get later on the other cases, you know, that are mixed between universals and singulars. You can get, you know, a particular affirmative and a particular what, negative, right?

[27:43] But this is really impressive, two universals, okay? Now, as they often tell the students, you know, if your parents are both negative, you're, not going to have any kids.

[28:01] But you can't get anything in two negatives, huh? because the set of all requires what, two affirmatives, right? If every B is an A, whatever is a B is an A. That's two affirmatives, right? But even the set of none, if no B is an A, whatever is a B is not an A. You've got to have something affirmative, don't you? So I'm suspicious that this two negatives would give you nothing.

[28:32] But. There's no way to get something following this. You can lay these down all day long, as far as I'm concerned, right? And you'll never what have something following what necessarily, right? Well, I'm from Missouri, and you got to prove it, right? Okay. Now, I'm going to

[29:00] use the if then again, which I'm very fond of that stuff, right now. Okay. If something follows necessarily, right? It will always follow, right? Something is necessary, right? It's always so, right?

[29:26] If four is necessarily what, half of eight? Every four will be half of eight, right? There will be some fours that are half of eight and some that are not, right? Some men that are women, and some women that are men. I told you Warren's experience there in the University of Wisconsin, there, right? And taking courses there, was denied when he was searching, right? So Warren, Warren, did, you know, contradicted him and said, and he said, "Give me an example, you know."

[30:03] Well, two plus two is four. That's the simplest one Yeah. And so he was a professional artist, a mathematician. He said, "What depends upon the system?"

[30:17] Depends upon the system, right? He says. So I suppose it depends on the universe. You got five, one, two, three, right? So. You had two, two. You had two, two. What? Two. You get what? One. One. That's stupid.

[30:40] You know. What are you doing? It's kind of like doing binary stuff. Nothing personal. It's kind of funny that you read about teachers and sometimes, so you know, they'll say like you know, you say for example that it's certain that the interior angles of the triangles are two right angles, right? And they'll say, well, I'll take the the triangle, you know, on the surface of the earth, right, the surface of the sphere, and you draw two lines down from the north pole to the what um...

[31:24] Equator. equator, right? And they would both seem to be making right angles, wouldn't they, with the north, with the the equator, right? And then you got the one up there you know, these two meet up at the north pole. So sometimes the triangle has more than two right angles. We're using the word triangle in an equivocal sense, right? The most common fallacy, right?

[31:52] So you want to find examples. You want to find examples where, when you put them into this form, right, the statements will be what true, right? Okay. But

[32:18] you want to have one set of examples where every C is A is in fact the case, right? And one example where no C is A, right? Because if every C is A is true just once, it's going to be what

[32:38] make two negatives, not always so. And if no C is A is true just once, maybe just once that this is so. And sometimes both affirmatives, universal, and, particular, are not so, right? And therefore, nothing affirmative, nothing negative is so always. And if nothing is always so, it's nothing is necessarily so, right? But that's a valid form, right? If A is so, B is so, B is not so, therefore, if it's always, if it's necessarily so, it's always so, right?

[33:16] It's not always so, therefore, it's not necessarily so. Therefore, it ain't a syllogism, because a syllogism is a speech or an argument in which some statements lay down, right? Another follows necessarily because of those laid down.

[33:34] So after we get used to finding these examples, and it's better to take very simple examples, right? Can you think of a b that is never an a?

[33:45] Yeah, let's take a stone, right? Mm-hmm. And we'll take what tree. We'll take three, okay. Oh stone is a tree. Now I want to find two examples for c. Neither which is a stone, but one is always a tree, right? Okay. So if we take let's say an oak tree, right?

[34:14] Every oak tree, or no oak tree, is a stone, and no stone is a tree. But every oak tree is a what? Tree. And then take what cat, I say, right? No cat is a stone, and no cat is a what Tree. Tree. So now if I satisfied my two conditions? Are the premises, in fact, true when substituted in those examples? Well, we all make stupid mistakes, so let's just check our work here.

[34:49] No b is a. No stone is a tree. Is that true? Yeah. And no c is a b. No oak tree is a what stone? That's true. No cat is a stone. Okay. I satisfied the first condition, right? Now do I have one example where every c is a?

[35:15] Yeah. So encircle that, right? Every oak tree is a tree. Well, that means that no negative statement is always the case. So there's no negative statement. I now know that follows necessarily. Even though I got two universal negatives. My God, you can't get a negative statement from two neg universal negatives, but

[35:38] we can get. Yeah. And do I have one example where no c is what? Yeah, underline that example, right? And no cat is a tree. if Sometimes, at least just once, I got one example. That's all I need. Um, can kill you know something with just one stone sometimes. Um, then any what affirmative statement is not true always, right? Okay. It's not always the case that every c is a.

[36:13] Not always the case that some c is a. Boom. So I've knocked out all universals. I mean, all affirmatives and you know negatives and all affirmative statements, right? So there's nothing. You can't say that every c is a. You can't say what some c is a. You can't say that no c is a is always the case, or some c is not a is always the case.

[36:42] Because sometimes every c is a, right? So I've eliminated that. Sometimes you need what Disjunctive syllogism too, right. Okay. I- I've eliminated all the possibilities, right? What follows necessarily is c and a. Well, if you say every c is a or some c is a, boom, that's gone. If you say it follows that no c is a or some c is not a, boom, you're finished. Admit defeat.

[37:14] Okay. So no syllogism right? huh Which I suspected because how do you get the even set of none out of this? You can't. You can't. have An affirmative, right?

[37:30] You know, so you're currently seeing something about the superiority of affirmative to the what negative, right? You can get a conclusion sometimes from a negative and a affirmative statement, but from two negatives, you can never get anything. Okay. So one of your parents is affirmative, at least to some hope. Get some negative children.

[37:56] Okay. Now, every B is A, no C is B, right? Can you repeat this up here? No C is A, right? Well, the set of none you'd have to try for, right? But

[38:16] you could get the statement if you went to some A is C, right? Or not C, right? If I turn this thing around, right? Okay. But is there any conclusion with C as a subject and A as a what predicate that's the thing we're asking?

[38:36] Well, you don't have it set up for the set of none because nothing is said to be a C, right? So if you can't get a conclusion with C as a subject and A as a predicate, we will take what

[38:57] examples for A, B, and C that satisfy two conditions, right? Every B is an A. Let's take animal, dog, I'd say, right? And then no cat is a dog, and no stone is a dog, right? Okay.

[39:22] So let's talk. If you substitute in these examples, every B is A, every dog is an animal, that's true. No cat is a dog. No stone is a dog. Okay, those are true. So there's no difficulty in the matter, right? Now, they have one example where every C is an A. Yeah, I'll stick with that one. Every cat is an animal, right? And one where no C is an A.

[39:51] Yeah, no stone. I'll underline that. So this knocks out any negative statement from being always the case. This knocks out any affirmative statement from always being the case. Together, they knock out both any affirmative or any negative. Well, that's all you have is affirmative and negative. But that exhausts the possibilities, right? Can't have any conclusion with C as a subject and A as a predicate if you can't have any affirmative and any negative, right?

[40:21] So the ball game is over, right? So I kind of accused of the either or dilemma, right, as well as the S and N, right?

[40:38] So the four universal cases of the first figure, two of them are what syllogisms, and two of them are not. But you have one for universal affirmative and one for universal negative. That's simple enough, right?

[41:17] Now, the second figure, right? You have it in the form of the middle term, and the term is common to both. You could say, right? If I'm not picky about it, it's the predicate in both cases, right? So you have every A is B, and every C is B.

[41:48] And you have the two negatives here: no A is B, and no C is B. Okay. And you have the mixed ones, right? No A is B, and every C is B. And you have the reverse: every A is B, and no C is B. Right. That's all the cases: the two universals, right, in the second figure. Now Aristotle calls these imperfect syllogisms because the set of all and the set of none, which are the basis for necessity, right, they don't apply to it as it stands, right?

[42:46] You have a what universal affirmative here: every A is B, but nothing is said to be an A. Universal affirmative here: every C is a B, but nothing's said to be a C. Okay. Now, if you could turn this around and say that every B is an A, and you could syllogize that every C is an A, right? You'd be back in the first figure, right? But can you necessarily necessity is what we're demanding, right?

[43:19] Now we're very vigorous, right? Very vigorous here. Can you necessarily turn around the universal affirmative? So how many examples do you have to show that it ain't always the case? See, every two is half of four, and everything half of four is two, right? You turn it around sometimes because of the matter, right? But can you always turn it around? Every dog is an animal. Every animal is a dog.

[43:50] No. Every odd number is a number. Every number is not a number, right? So I suspect you can't get anywhere even by conversion, here, right? I regret to say it, but I'm afraid that it's invalid, right? Well, I'm from Missouri. You got to prove to me, right? So, how do you prove that nothing follows necessarily here? Well, not getting too pedantic.

[44:26] You got to find examples for A, B, and C such that when you substitute them in here, these will be true, right? Because you want to make sure that there's no defect in the matter, right? Now, the two purposes of trying to make the form invalid because the matter is bad, right? Don't you try to pull that trick on your opponent? I want examples, right, where the matter is perfect.

[44:52] Okay. So, so we say every dog is a what? Every what? Copper Spaniel. it's a, I don't know what it means here. Yeah. Copper spaniel, right?

[45:17] Is an animal, right? And then every cat is an animal, right? Now, I make stupid mistakes. We all make stupid mistakes, right? We should know better, right? So, do I satisfy the two conditions? Are the premises true when you substitute those examples in? Every A is B. Every dog is an animal. That's true. Every C is B. Every copper Spaniel is an animal. Yeah. Every cat is a what?

[45:50] Animal. Animal. Yeah. I have satisfied the first condition with these examples. The premises are the matter is perfect. The matter is perfect, right? Okay. Now, do I have one example where every C is A? Yeah. Every cocker. I'll circle that, right? Every cocker spaniel is a dog, right? Do I have one example where no C is A? Yeah. No cat is a dog, right?

[46:19] So this knocks out any what? Negative statement. This knocks out any affirmative statement. And if there's no negative or affirmative statement. Then you can't say necessarily anything. This C is a subject, and A is a predicate. You can't say that every C is A or some C is A, because of this. You can't say that no C is A and some C is A or is not A, because sometimes every C.

[46:50] So there's nothing you can do, right? Exhausted you, right? Okay. But now, how about over here? No A is B, and every C is B, right? Well, as it stands, the set of none doesn't apply, does it? You do have a universal negative, no A is B, but is anything said to be an A? No. But can you convert? No A is B to no B is A.

[47:33] Now, that's I'm not sure what that purpose is. I don't accept that. I'm from Missouri. How do you know you can turn that around? I just I put an assumption in the part of the prerequisite. Well, you worked at Assumpton College, so that works. That's appropriate.

[47:56] I want you to prove to me that if no A is B, then no B is A. That's quite a demanding thing, right? Because I mean, there's an infinity of the statements that could be in the form no A is B, right? Why don't you show me in every one of those examples for no A is B? Yeah? I mean no dog is a cat, no cat is a dog, right?

[48:22] Circle is a square and square is a circle. Yeah, but you know, there's an infinity of universal negative statements, right? I can't go through them all, right? Okay, gotcha, Burkus.

[48:37] You make that claim, you ain't got ever stop, right? See? I maintain that if no A is B, then no B is A. Now, if you say that ain't necessarily so,

[48:54] that it's possible when no A is B that some B, at least one B, is what A, right? Well, let it happen. You say it could happen, right? It ain't necessarily in this case. Now, some B is A. Let's give a name to the B that is an A. Even just one single B, right? We'll call the the some B that is an A X, right? Then X is both a B and what A and a.

[49:31] Okay? Because you said there could be some B, at least one B, that is an A, right? And so if you call that B that is an A X, since it's a B that is an A, it's both a B and an A, isn't it? Therefore, there's some A that is what B, which X. If X is both A and B or B and A, then there's some A that is a B.

[50:00] But that contradicts this, right? Can some A be a B when no A is a B? Impossible. Yeah. That goes back to the axiom, you know, a contradiction, right? No A is B and some A is B, contradictory. Can't stand it. So you would contradict this unless you admit this, right? If you deny this, you have to admit this by contradiction, and then you end up with something being both a b and an A, And then you end up contradicting that, so you're forced by the truth itself, right?

[50:36] Okay. Thomas is, you know, I was reading the twenty second question there, of the De Veritate, bonitate I call it, you know, because it starts with the later on. He's talking about, you know, can can you coerce the will? Right? He's arguing you can, right? But you can, in a way, coerce the the mind, right? You know, because sometimes the mind doesn't want to admit something, you know, and then you're forced by the truth itself, right?

[51:07] Now to admit that it's true, so this guy didn't want to admit it. You turn this around. He thought it was making a wild leap, right? But now he's shown that he must admit that, right? Now, forcing him against his will, right?

[51:27] I told you I had a student out in California. You know, he always come in almost every class with an objection. You know, I'd read all the things, and you know, it wasn't the most difficult to solve yet. But one time we had a conversation something after the course was completed. You know, and so on. He said, "I was shocked today." You know. But he's a good student, though, right?

[51:49] And and and when I started to find he'd be fighting for it, and as I gradually, you know, resolved his objection, you know, he seemed pretty relaxed. We didn't, you know, have a story that he turned your toes. Yeah. I just kind of kick out of him in the

[52:06] sense. So if you can turn this around, then you got no B is a, and just keep every C is B, and lo and behold, by magic, by conversion, at least if not by magic, you are in what figure now? First, yeah. It's obvious now that no c is what. No c is a, right? So it follows necessarily that no c is a, but it's not quite as clear as the first figure.

[52:39] You have to convert in order to make it clear that the dictum de omni or the dictum de nullo the set of none in this case applies, right? And you get back to the first figure. So the first figure, right, is called first, right? Now, start like this: looking before and after, right?

[53:00] Now, can I turn this around and get a conclusion with that no c is a? Well, I can't work this out with the set of all, obviously. I can't use a set of none here because nothing is said to be a C, right? But I could turn this over into what? No B is C,

[53:42] and keep every A is B, right? Now, if, no B is a C, but every A is a B. Then what? If every, if no B is C, and every A is a B, then what? No A is C. Yeah, but I want something with C as a subject, right? A as a predicate. Oh, but I can take two steps. I have to convert twice, right? So it does follow that no C is A, but I got to, oh my God, twice, right?

[54:21] But I get something like the first figure in both cases, right? Okay. Okay. Here, sorry, let's make the first figure. You have C and A in the wrong positions. Okay. So

[54:38] I can get universal negative from perhaps just in this form and one in this form, right? I remember when I was a young philosopher and learning logic a little bit, and actually, you know, when Richard started teaching me logic, I was in high school there, you know. So I came into college and to give me the final exam.

[55:07] Didn't do it. They give me credit for the course that I'm taking, right? But when I got thinking, you know, about you know the God and so on, right? Well, God is not a universal, right? Every God is pure act, but this individual God, right, is pure act, right? But can you convert, you know, a the singular like that?

[55:36] If you say that God is is is not composed, can you turn it around and say that that's true? That God is not composed. That nothing composed is God.

[55:51] Yeah. Because if something composed was what God, then God would be in that case we call X the thing composing that is God, and then both God and composed, and then God is what composed. So you can convert that, right? I'll take a simpler example here. Socrates is not a what? Woman. You turn it around and say the woman is Socrates,

[56:28] because if you don't admit the woman is Socrates, then some woman could be Socrates, right? Some woman is Socrates. Let's give her her name. Call her X, right? Well, X is both a woman and Socrates. Therefore, Socrates, whose X is a woman, and you said Socrates is not a woman, right? Okay, so you can turn around, you know. Well, that was important for me to see that you still treat God, right?

[56:55] You can what treat God is not composed, and turn around and say that composed is God, right? God is infinite. Nothing finite is God, right? Okay.

[57:14] But here, in the Peri Hermeneias he was concerned with universal statements right? Okay. Okay now. Negative parents. Oh my God! What do you do with negative premises Can't do anything with them, right?

[57:34] Because even for the sin of none, you've got to have an affirmative statement, right? So we expect you to find examples for A, B, and C to prove that this is nothing, right? Nothing down here, right? Nothing follows necessarily. Okay, this is kind of simple stuff, right? You take animal, right? And take stone. And take cat and what? Tree. Tree. Okay. Now, to avoid stupid mistakes, you always check your material.

[58:15] No A is B. No animal is a stone. That's true. No C is B. No cat is a stone. That's true. No tree is a stone. That's true. So with these examples, the premises are true. The matter is perfect, right? So if there's any defect, it can't be the matter. My matter is perfect. Okay.

[58:41] If you have an argument that no animal is a stone and no cat is a stone, you might say, "Can you prove from that that every cat is an animal?" Well, it might be that no C is an A, right?

[58:57] So you have one example where every C is an A, and that means that no negative statement is always the case. No tree is a what? Every is an animal. Therefore, no affirmative statement is always the case, right? So no affirmative and no negative statement is always the case, and therefore none of them can be what necessarily following, right? So nothing follows necessarily.

[59:30] Okay It ain't the syllogism, right? It isn't a syllogism, is it?